Fluid or chemical injection valves for controlling the flow of fluid between the annulus between the well tubing and the well casing and the inside of the tubing are old. Typically, such valves are spring-loaded relief valves which are installed in the tubing string with the valve sealing off a port that communicates between the interior of the tubing and the annulus between the tubing and the casing. In one type of valve, the valve is set to a desired opening pressure and will open and allow fluid to be injected into the tubing when the annulus pressure exceeds the tubing pressure by the present value. In another type of valve for injecting chemicals from the tubing to the annulus, the valve is actuated when the tubing pressure exceeds the annulus pressure by a present value. However, it is a common practice to install a safety valve in the flow of well production below the injection valve. If the safety valve closes, the pressure above the safety valve and adjacent the injection valve drops considerably. When this happens, the differential between the casing annulus pressure and the tubing pressure changes proportionately thereby causing the injection valve to open and increases the flow of fluid through the injection valve. Since a typical installation may have several thousand feet of chemical fluid acting against the valve inlet, the fluid creates a hydrostatic pressure at the injection valve depth. The opening pressure of the injection valve is usually set so that a minimum of surface injection pressure in addition to the hydrostatic head is required to open the injection valve at normal producing pressure valves. Therefore, if the normal producing tubing pressure falls as a result of a subsurface safety valve closure, the hydrostatic head of the injected fluid may flow through the injection valve causing the loss of considerable fluid and possibly loading up the flow of well production so that the well cannot produce. The present invention is directed to an improved fluid or chemical injection valve which provides a closure force sufficient to overcome the hydrostatic head of the injected fluid in the event that the producing well pressure drops a predetermined amount below normal producing well pressure values.